This is where I get this question from
It looks like a special type of positions that required some pass moves to reach (with several different ways), so in a sense there are definitely positions that can be categorized as “normal”, and some that required multiple pass moves to reach (including most tusmego positions). They can even be further divided into at least 1, 2, 3, etc. pass moves to reach. Although they are definitely finite, but not feasibly possible to give numbers to. Can we even reasonably estimate the portion of them?
And my intuition would say the “normal game play” positions are comparably very few to all possible positions, but what’s the portion be like? I have no idea. Not even an educated guess in range.
The positional super-ko repeating cycle length problem is even harder, I don’t even know where to begin.